[Satellite Communications] Link Budget/Link Margin Calculation/Signal-to-Noise Ratio and Carrier-to-Temperature Ratio (Updated)

2023.06.27 I recently learned some knowledge about satellite communication link budget. I also knew it before, but the entire knowledge system was not well established. Therefore, I consulted some literature and sorted out the relevant knowledge completely (the content involved was not in-depth. for reference only.)

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Preface

These are some notes during the learning process. It is not easy to edit formulas in markdown. Please click like it with your fingers!

1. (G/T)/EIRP

1.1 Quality factor (G/T)

  Earth stations mainly use the quality factor G/T value (receiving antenna gain to noise temperature ratio) to describe the receiving performance of the ground station . The higher the G/T value, the stronger the receiving performance. Regarding power amplifiers: Small ground stations use solid-state power amplifiers of 0.25W; large ground stations use traveling wave tubes or klystron amplifiers (10-15kw). The figure below is the schematic block diagram of the earth station equipment.

1.2 Effective Isotropic Radiated Power/EIRP

Effective omnidirectional radiated power describes the transmission performance of the ground station . The formula is expressed as:
$$EIRP=P_T\cdot G_T=High\; power\; amplifier\; output\cdot Antenna\; gain\text{\hspace{1em}( 1 )}$$ If the antenna gain is written in dB, the unit should be dBi. Sometimes it is necessary to consider the loss from the power amplifier output to the antenna. In most areas of our country, EIRPs (s=satellite) are above 32dBW.

2. Transmission equation

2.1 Transmission equation

$$C=P_T\cdot G_T\cdot G_R/L\text{\hspace{1em}( 2 )}$$ Among them, C is the carrier power received by the receiving ground station,$P_T$is the isotropic point source transmitting power, $G_T$with $G_R$are the transmitting and receiving antenna gains respectively, d is the transmission distance (radiated outward in the form of a sphere); L represents the transmission loss, of which the free space propagation loss is often L f $L_f$警代表，$L_f=(4pd/l{)}^{2.}$ In addition to free space propagation loss, atmospheric absorption loss, clouds, rain attenuation, atmospheric refraction, ionospheric scintillation and multipath must also be considered (other losses besides free space propagation loss are often collectively referred to as link additional losses). The form written in decibels is:
$$C(dBW)=P_T(dBW)+P_T\left(dBW\right){+}_T\left(dBW\right)-20lg(4pd/l)\text{\hspace{1em}(3)}$$

2.2 System noise

  The noise studied in communication systems is generally based on white noise (the power spectral density is constant, assumed to be N0/2). After the noise in figure a passes through an ideal bandpass filter such as b, the output noise power is: N $N=2\cdot \frac{N_0}{2}\cdot B=N_0\cdot B=k{T}_{s}B\left(W\right)$ , where k is Boltzmann's constant, Ts is the equivalent noise temperature of the link (K=C+272.15), and B is the bandwidth of the bandpass filter (can also be understood as the equivalent noise bandwidth).

3. Link budget and link margin

Link budget: The information we transmit to the destination must have a certain degree of fidelity, so the link budget is to accurately calculate the link carrier-to-noise ratio and link margin to ensure the normal operation of the satellite communication system in actual projects. The link loss calculation formula for uplink and downlink (u/d for short):
$$\begin{array}{c}{\text{L}}_{\text{u}}={\text{L}}_{\text{fu}}+{\text{L}}_{\text{au}}+{\text{L}}_{}+{\text{L}}_{}+{\text{L}}_{\text{ru}}\text{(dB)}\\ {\text{L}}_{\text{d}}={\text{L}}_{\text{fd}}+{\text{L}}_{\text{ad}}+{\text{L}}_{}+{\text{L}}_{}+{\text{L}}_{\text{rd}}\text{(dB)}\end{array}\text{\hspace{1em}( 4 )}$$

  As can be seen from the above figure, the uplink and downlink losses, the quality factor of the ground receiving station, the equivalent isotropic radiated power of the ground transmitting station and the equivalent isotropic radiated power of the satellite transponder jointly determine the satellite uplink and downlink Road load-to-noise ratio. Among them, the carrier-to-noise ratio of the uplink and downlink are respectively expressed as:$$\begin{array}{c}{\left[\text{C}/\text{N}\right]}_{\text{u}}=\text{EIR}{\text{P}}_{\text{t}}-{\text{L}}_{\text{u}}+{\left[\text{G}/\text{T}\right]}_{\text{s}}-10\text{lg}\left(\text{kB}\right)\left(\text{dB}\right)\left(Think\; of\; satellites\; as\; receiving\; stations\right)\\ {\left[\text{C}/\text{N}\right]}_{\text{d}}=\text{EIR}{\text{P}}_{\text{s}}-{\text{L}}_{\text{d}}+{\left[\text{G}/\text{T}\right]}_{\text{r}}-10\text{lg}\left(\text{kB}\right)\left(\text{dB}\right)(Think\; of\; satellites\; as\; transmitting\; stations\end{array}\text{\hspace{1em}( 5 )}$$
The total carrier-to-noise ratio can be obtained by adding uplink and downlink:$$\begin{array}{rl}& \frac{1}{{\left[\text{C}/\text{N}\right]}_{}}=\frac{1}{{\left[\text{C}/\text{N}\right]}_{\text{u}}}+\frac{1}{{\left[\text{C}/\text{N}\right]}_{\text{d}}}\\ & {\left[\text{C}/\text{N}\right]}_{}=\frac{1}{{\left[\text{C}/\text{N}\right]}_{\text{u}}^{-1}+{\left[\text{C}/\text{N}\right]}_{\text{d}}^{-1}}\left(\text{dB}\right)\end{array}\text{\hspace{1em}( 6 )}$$
Finally, the link margin can be calculated: link margin =$[C∕N]$ -Receiving station demodulation threshold (defined according to actual situation)

4. Carrier-to-noise ratio/signal-to-noise ratio/ $E_b/N_0$/load temperature ratio

4.1 Carrier-to-noise ratio and signal-to-noise ratio

  First of all, we need to understand clearly what the definitions of the two are. Signal-to-noise ratio S/N: the ratio of the average power of the transmitted signal to the average power of the additive noise; carrier-to-noise ratio C/N: the ratio of the average power of the modulated signal (including the transmitted signal and the modulated carrier) to the average power of the additive noise. From a definition point of view, the difference between the two is the power of the modulated carrier. Therefore, in modulation transmission systems, the carrier-to-noise ratio index is generally used; while in baseband transmission systems, the signal-to-noise ratio index is generally used. In actual communication scenarios, the carrier power is usually very small compared to the transmission signal power, so the carrier-to-noise ratio and the signal-to-noise ratio are very close in value, that is, S/N ≈ C/N. Since satellite signals are generally modulated signals , so the carrier-to-noise ratio is commonly used in link budgets.
  Continuing to expand, let’s talk about the relationship between SNR and Eb/N0. In digital communication scenarios, since the bandwidth and transmission rate of the system are often different, it is difficult to compare horizontally. Therefore, SNR is generally not measured but Eb/N0. The two The relationship: $$SNR=\frac{\text{S}}{\text{N}}=\frac{{\text{E}}_{\text{b}}\cdot {\text{R}}_{\text{b}}}{{\text{N}}_0\cdot \text{B}}=\frac{{\text{E}}_{\text{b}}}{{\text{N}}_0}\cdot \frac{{\text{R}}_{\text{b}}}{\text{B}}\text{\hspace{1em}(7)}$$

4.2 Load to temperature ratio

  Since the carrier-to-noise ratio is a function of bandwidth B, it is inconvenient to compare systems with different bandwidths. Therefore, this representation method lacks versatility. In addition, the noise suffered by the link can be equivalent to the noise temperature of the receiving end, so link performance often uses carrier temperature. Ratio C/T means that the conversion relationship between C/N and C/T is:
$$\left[\frac{\text{C}}{\text{N}}\right]=\left[\frac{\text{C}}{\text{cBT}}\right]=\left[\frac{\text{C}}{\text{T}}\right]-\left[\text{k}\right]-\left[\text{B}\right]\text{\hspace{1em}(8)}$$因此可以将式(8)整理为：
$$\begin{array}{c}{\left[\text{C}/\text{T}\right]}_{\text{u}}=EIR{\text{P}}_{\text{t}}-{\text{L}}_{\text{u}}+{\left[\text{G}/\text{T}\right]}_{\text{s}}\left(\text{dB}\right)\\ {\left[\text{C}/\text{T}\right]}_{\text{d}}=EIR{\text{P}}_{\text{s}}-{\text{L}}_{\text{d}}+{\left[\text{G}/\text{T}\right]}_{\text{r}}\left(\text{dB}\right)\end{array}\text{\hspace{1em}( 9 )}$$ The above is in the form of a single carrier. In a multi-carrier system, the above equation needs to be modified:
$$\begin{array}{c}{[\frac{\text{C}}{\text{T}}]}_u=EIR{\text{P}}_{ES}-{[BO]}_{oe}-\left[{\text{L}}_{\text{u}}\right]+\left[\frac{{\text{G}}_{RS}}{{\text{T}}_{\text{s}}}\right]\\ {\left[BO\right]}_{oe}Compensation\; for\; earth\; station\; amplifier\; output,EIR{P}_{ES}\text{is the EIRP of the earth station when the transponder is saturated}\\ {\left[\frac{\text{C}}{\text{T}}\right]}_{dm}=EIR{\text{P}}_{SS}-{\left[BO\right]}_{\text{O}}-\left[{\text{L}}_{\text{d}}\right]+\left[\frac{{\text{G}}_{RE}}{{\text{T}}_{\text{E}}}\right]\\ {[BO]}_{o}is\; the\; transponder\; output\; compensation,T_E\text{is the earth station equivalent noise}\end{array}\text{\hspace{1em}( 10 )}$$
At this point, the basic link budget has been completed. Next, it is necessary to consider whether to add interference according to the actual situation of the system (for example, the intermodulation interference generated between nonlinear power amplifier carriers, the interference caused by adjacent stars to the ground station antenna) Interference, cross-polarization interference between co-frequency carriers of different plans, etc. For detailed calculation process, please refer to [2])

5. Supplement

5.1 Free space propagation loss (formula derivation)

In the process of working on the project, I saw two formulas for free space propagation loss: I always thought it was a clerical error in the book, but I deduced it myself and found that it was not the case ( $f$ and$Different\; units\; of\; d$ will lead to changes in the previous coefficients) so record it (refer to [5]).
$$\begin{array}{rl}& Lbs(dB)=10\lg (\frac{4p}{3\times 10^8}{)}^2\\ & Lbs\left(dB\right)=20\lg \frac{4p}{3\times 10^8}\\ & Lbs\left(dB\right)=20\lg \frac{4\pi \left(d\right(km)\times 10^3)(f(MHz)\times 10^6)}{3\times 10^8}\\ & Lbs\left(dB\right)=20\lg \frac{4\pi d(km)f(MHz)\times 10^9}{3\times 10^8}\\ & Lbs\left(dB\right)=20\lg \frac{4\pi d\left(km\right)f\left(MHz\right)\times 10}{3}\\ & Lbs\left(dB\right)=20\lg \frac{4}{3}+20\lg d\left(km\right)+20\lg f(MHz)+20\lg 10\\ & Lbs\left(dB\right)=12.45+20\lg d\left(km\right)+20\lg f\left(MHz\right)+20\\ & Lbs\left(dB\right)=32.45+20\lg d\left(km\right)+20\lg f\left(MHz\right)\\ & Lbs\left(dB\right)=32.45+20\lg d\left(km\right)+20\lg f(GHz)+20\lg 1000\\ & Lbs\left(dB\right)=32.45+20\lg d\left(km\right)+20\lg f\left(GHz\right)+60\\ & Lbs\left(dB\right)=92.44+20\lg d\left(km\right)+20\lg f(GHz)\end{array}\text{\hspace{1em}(10)}$$

references

[1] Zhang Ming. Research on optimization algorithm for equivalent isotropic radiated power estimation in satellite link budget [D]. Shanghai Normal University, 2022.DOI:10.27312/d.cnki.gshsu.2022.000461. [2] Hu Lingzhi, Zhang
Haiyong , He Yin. Research on calculation methods of satellite communication links [J]. Ship Electronic Engineering, 2019, 39(11): 72-75.
[3] What are the signal-to-noise ratio S/N, carrier-to-noise ratio C/N and Eb/N0? _Lele Pingping's dad's blog - CSDN blog
[4] Link budget online calculator
[5] Free space loss formula derivation process and simple usage
[6] Reference book "Satellite Communication Systems and Technology" Author: Chen Zhenguo, edited by Guo Wenbin Beijing University of Posts and Telecommunications Press